C Library Functions - weicdf (3)

NAME

weicdf(3f) - [M_datapac:CUMULATIVE_DISTRIBUTION] compute the Weibull cumulative distribution function

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE WEICDF(X,Gamma,Cdf)

       REAL(kind=wp),intent(in)  :: X
       REAL(kind=wp),intent(in)  :: Gamma
       REAL(kind=wp),intent(out) :: Cdf

DESCRIPTION

WEICDF(3f) computes the cumulative distribution function value for the Weibull distribution with REAL tail length parameter = GAMMA.
The Weibull distribution used herein is defined for all positive X, and has the probability density function
       f(X) = GAMMA * (X**(GAMMA-1)) * exp(-(X**GAMMA))

INPUT ARGUMENTS

X The value at which the cumulative distribution function is to be evaluated. X should be positive ( >0 )

GAMMA The value of the tail length parameter. GAMMA should be positive.

OUTPUT ARGUMENTS

CDF The cumulative distribution function value for the Weibull distribution

EXAMPLES

Sample program:

   program demo_weicdf
   !@(#) line plotter graph of cumulative distribution function
   use M_datapac, only : weicdf, plott, label
   implicit none
   real,allocatable  :: x(:), y(:)
   real              :: gamma
   integer           :: i
      call label(’weicdf’)
      x=[((real(i)+epsilon(0.0))/30.0,i=0,100,1)]
      if(allocated(y))deallocate(y)
      allocate(y(size(x)))
      gamma=12.2
      do i=1,size(x)
         call weicdf(X(i),Gamma,y(i))
      enddo
      call plott(x,y,size(x))
   end program demo_weicdf

Results:

The following is a plot of Y(I) (vertically) versus X(I) (horizontally) I-----------I-----------I-----------I-----------I 0.3333333E+01 - X 0.3194444E+01 I X 0.3055556E+01 I X 0.2916667E+01 I X 0.2777778E+01 I X 0.2638889E+01 I X 0.2500000E+01 - X 0.2361111E+01 I X 0.2222222E+01 I X 0.2083333E+01 I X 0.1944444E+01 I X 0.1805556E+01 I X 0.1666667E+01 - X 0.1527778E+01 I X 0.1388889E+01 I X 0.1250000E+01 I X 0.1111111E+01 I X X X 0.9722223E+00 I X X X X 0.8333335E+00 - XX X X X 0.6944444E+00 I XX 0.5555556E+00 I X 0.4166667E+00 I X 0.2777779E+00 I X 0.1388891E+00 I X 0.3973643E-08 - X I-----------I-----------I-----------I-----------I 0.0000E+00 0.2500E+00 0.5000E+00 0.7500E+00 0.1000E+01

AUTHOR

The original DATAPAC library was written by James Filliben of the Statistical Engineering Division, National Institute of Standards and Technology.

MAINTAINER

John Urban, 2022.05.31

LICENSE

CC0-1.0

REFERENCES

o Johnson and Kotz, Continuous Univariate Distributions--1, 1970, pages 250-271.

o Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, page 124.

Nemo Release 3.1

weicdf (3)

July 22, 2023

Generated by manServer 1.08 from 5622398c-3ebe-4371-9b5e-01806bbeb7ad using man macros.

X	The value at which the cumulative distribution function is to be evaluated. X should be positive ( >0 )
GAMMA	The value of the tail length parameter. GAMMA should be positive.

o	Johnson and Kotz, Continuous Univariate Distributions--1, 1970, pages 250-271.
o	Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, page 124.